Active control of the synchronization manifold in a ring of mutually coupled oscillators

We investigate the active control of synchronization dynamics in a shift-invariant ring of N mutually coupled self-sustained electrical systems. Using the master stability function approach, we derive the regime of coupling parameters leading to stable and unstable synchronization phenomena in the ring. The active control technique is applied on the mutually coupled systems to suppress undesired behavior, such as the unstable synchronization manifold. We derive the range of control gain parameters which leads to a successful control and the stable control design. The effects of the control or gain parameters on the stability boundaries of the synchronization process are also studied.